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Chapter 35: Q19P (page 1075)

Suppose that Young’s experiment is performed with blue-green light of wavelength 500 nm. The slits are 1.20 mm apart, and the viewing screen is 5.40 m from the slits. How far apart are the bright fringes near the center of the interference pattern?

Short Answer

Expert verified

The bright fringes near the center of the interference pattern are apart of 2.25 mm.

Step by step solution

01

Write the given data from the question

Blue-green light Wavelength, λ=500nm.

The slit separation, d=1.20mm.

The screen distance from the slit, D=5.4m.

02

Determine the formulas to calculate how far apart the bright fringes near the center of the interference pattern

The condition for the maxima in Young’s experiment is given as follows.

dsinθ=mλ …… (1)

Here, d is the distance between the slits, λis the wavelength, mis the order, andθis the angular separation.

03

Calculate how far apart the bright fringes near the center of the interference pattern

The maximum vertical distance from the center of the pattern is given by,

tanθ≈sinθ=ymD

Substitute ymDfor sinθinto equation (1).

dymD=mλym=mλDd

Substitute 1 for m, 54 m for D, 500 nm for λand 1.20mmfor d into above equation.

ym=1×500×10-9×5.41.2×10-3=27×10-71.2×10-3=22.5×10-4m=2.25mm.

Hence the bright fringes near the center of interference pattern are apart of 2.25 mm.

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Most popular questions from this chapter

Find the slit separation of a double-slit arrangement that will produce interference fringes0.018 radapart on a distant screen when the light has wavelengthλ=589 nm.

Monochromatic green light, of wavelength 500 nm, illuminates two parallel narrow slits 7.70 mm apart. Calculate the angular deviation ( θin Fig. 35-10) of the third-order (m=3)bright fringe (a) in radians and (b) in degrees.

Figure 35-25 shows two sources s1 and s2 that emit radio waves of wavelengthλin all directions. The sources are exactly in phase and are separated by a distance equal to 1.5λ . The vertical broken line is the perpendicular bisector of the distance between the sources.

(a) If we start at the indicated start point and travel along path 1, does the interference produce a maximum all along the path, a minimum all along the path, or alternating maxima and minima? Repeat for

(b) path 2 (along an axis through the sources) and

(c) path 3 (along a perpendicular to that axis).

In Fig. 35-45, two microscope slides touch at one end and are separated at the other end. When light of wavelength 500 nm shines vertically down on the slides, an overhead observer sees an interference pattern on the slides with the dark fringes separated by 1.2 mm. What is the angle between the slides?

Transmission through thin layers. In Fig. 35-43, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. (The rays are tilted only for clarity.) Part of the light ends up in material 3 as ray r3(the light does not reflect inside material 2) and r4(the light reflects twice inside material 2). The waves of r3and r4interfere, and here we consider the type of interference to be either maximum (max) or minimum (min). For this situation, each problem in Table 35-3 refers to the indexes of refraction n1,n2and n3the type of interference, the thin-layer thickness Lin nanometers, and the wavelength λin nanometers of the light as measured in air. Where λis missing, give the wavelength that is in the visible range. Where L is missing, give the second least thickness or the third least thickness as indicated.
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